Present techniques for selecting among designs, and making other kinds of choices among alternatives, fail to deal very well with the fact that such problems are almost always multi-criterial. Often, improvements according to one criterion can be achieved only at a cost according to another criterion. In many instances, users are required to make mathematically convenient, but often inappropriate, assumptions. Traditional optimization approaches typically call for the user to assign an a priori weighting on the various criteria. The traditional approach to handling the multicriteriality of design generally treats the problem as one of optimizing a function composed of a weighted sum of the many criteria. However, assigning weights a priori is not the most natural thing for an engineer because the weights are nonlinear in the design space and are a function of what alternatives are available. There might not even be a need to trade-off criterion one against criterion two, depending on what is available.
Design as a practice generally involves incremental change. When a new design problem comes up, typically designs that have done well for a similar class of problems are incrementally modified. As new technologies for some of the components are introduced, potentially new possibilities open up the design space, but in practice, the impact of such innovations take a long time to filter to the design of the device or system as a whole, because changes are made incrementally.
Pareto optimality, as a kind of multiple-objective, or multiple criteria optimality has been considered extensively, and there is substantial prior art in this area. Techniques have been developed for generating some or all elements of a Pareto-optimal set, and for ordering or selecting from the Pareto-optimal set. Much of the work in the field has treated the problem of generation in the context of continuous function optimization, i.e., it has treated the domain of alternatives as being an n-dimensional continuous space. Then, the emphasis is laid on efficiently identifying the Pareto surface mathematically, or more commonly, some of the elements in the Pareto set. A common technique is to try to convert the problem into a standard function-optimization problem by asking the decision-maker for the relative importance of the criteria in the form of weights, and formulating a new criterion that is a linearly weighted combination of the original criteria. But such weights are notoriously hard to elicit from users, and in any case, decision-makers' preferences are typically not linear over the space of alternatives.
Even when the choice space is modeled as a discrete set of alternatives, the alternatives are not considered massively or exhaustively because the computational cost has been considered to be too high. Typically, techniques are proposed to generate, efficiently, a few of the Pareto-optimal elements rather than the entire set. In general, the major goal is viewed as reducing the computational load in considering alternatives. Although the use of filters has been proposed for reducing the number of alternatives, these proposals do not address the problems of errors and noise in the criteria values.
Whether or not some or all the Pareto-optimal elements are generated, there is still the problem of choosing from among them. There have indeed been a number of graphical approaches to this problem. Techniques such as value paths, bar charts, star coordinate systems, spider web charts, petal diagrams, scatterplot matrices, GRADS, harmonious houses, and Geometrical Analysis for Interactive Aid (GAIA) have been proposed. However, none of these techniques provide a mechanism for allowing the user to comparatively examine the various candidates and their interrelationships.